In this study, we propose an adaptive Fourier linear combiner (FLC) based on a modified least mean kurtosis (LMK) algorithm for canceling the sinusoidal noise signals from the desired signals. In the proposed framework, the weight coefficients of the FLC are adjusted by using the modified LMK algorithm instead of the conventional least mean square (LMS) algorithm. The fundamental reasons for using the proposed LMK algorithm in the FLC are that it provides a fast convergence rate, a lower steady-state error and a robust behavior against sinusoidal noise distributions. The performance of the proposed FLC algorithm is assessed on the noise canceling problem by comparing that of the conventional FLC based on the LMS algorithm. The simulation results demonstrate that the proposed FLC based the modified LMK algorithm outperforms its conventional LMS algorithm in terms of the convergence rate and the steady-state error.